Measuring Distances of Astronomical Objects

We are seeing astronomical objects which are billions of light years away (a light year is the

distance which light travels in one year, approximately 9.5 × 1012 kilometres). The light from

these objects needed billions of years to reach us. This shows that the universe that we are

seeing presently has to be billions of years old. However, how do scientists measure distances

of astronomical objects by using geometrical method?

In order to get to the distances of astronomical objects, ‘ladder’ methods have to be used

where there will be few different steps. And every latter step depends on the results of the

previous steps.

Firstly, there is the geometrical method to find the distance. To use this method, we need to

know the parallax of the star we wish to know the distance. How do we find the parallax?

The simple analogy is by looking at a certain object first by closing the right eye and then the

left eye. We will see that the position of the object differs. This is because our eyes have

different angles to the object (the difference is what is known as parallax). The distance

between the eyes is called baseline.

Stars are very distant from us and obviously eyes cannot be used to determine their parallax.

To measure the distance of a star, the position

of Earth during summer and winter will act as

our right and left eyes. The baseline of this

parallax would be the diameter of Earth’s orbit

passing through the sun. The length of the

baseline is 300 million kilometres (AU = 150

million kilometres). Parsec (parallax second) is

always used to measures the distances. 1

parsec is the distance of a star that has a

parallax of 2 arcseconds. 1 AU = 1 arcsecond

(one arcsecond is the 60th part of one

arcminute, and one arcminute is the 60th part

of one degree). Hence, a star with a parallax of

x arcsecond(s) is 2/x parsec away. X = α-β.

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However, using this parallax method, only stars with distances up to 10 light years can be

measured. The next step is by measuring the distances of as many as possible nearby stars to

get the value for the average density of stars (stars per cubic light year). Then, count the

visible stars and divide by the average density. This gives a (lower) bound on the size of the

universe. This method is applicable as the density of stars is more or less the same in all

regions where we can see stars. In 1989, satellite HIPPARCOS was launched. It measured the

positions, parallaxes and other parameters of close to 120,000 nearby stars. In 2010, satellite

GAIA was launched and is able to measure distant stars up to 10 kiloparsecs (32,600 light

years) away. Radio waves can measure smaller parallaxes without the use of satellites. It is

called ’Very Long Baseline Interferometry’ where 2 radio telescopes are placed on different

side of Earth. Distances to pulsars (stars which consist of mainly neutrons that emit radio

pulses regularly) can be measured.

The next geometrical method is one has to know the size of an object and the measurement of

angles at which one sees the 2 sides of the object. To get the size, the type of object (star,

galaxy and etc) and the parameters (luminosity, mass, angular distance to other object and so

on) has to be identified. With these data, a model is made and the size is extracted from the

model.

Next, to determine the distances of astronomical objects, scientists use the stellar photometry

and spectroscopy method. Stars which are so far away cannot be measured their parallaxes

(yet), therefore, the photometry is used, that is, by using the measurements of their

brightness. Photometry applies the inverse-square-law where the brightness decreases

proportional to the square of the distance. To use this method, the brightness of a star in a

fixed reference distance has to be determined to be compared with the measured star. The

standard reference distance used is 10 parsecs. Absolute brightness of a star is the brightness

it would be seen from the distance of 10 parsecs while apparent brightness of a star is the

brightness it would be seen from the Earth. Spectroscopy is used to know the absolute

brightness of a star. In the spectrum of a star, there will be some wavelengths that have dark

lines on them because lesser light is emitted. This phenomenon happens as the result of

absorption of light emitted by the atoms in the atmosphere of the star. Once those atoms are

excited, they emit the same wavelength which tells precisely which spectral lines belong to

which element. By looking at the dark lines in the star spectra, we can determine which

elements are in its atmosphere.

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All stars have groups known as spectral classes which each group has distinct pattern of dark

lines. The classes are labelled with capital letters: O, B, A, F, G, K, and M. Each spectral

classes are associated with a certain colours of the stars. Based on the theory of radiation,

colours depend on the surface temperature of an object. The highest temperature is for stars in

class O and decreases until the class M. The colours of stars are white (class O), then blue,

green, yellow (class G, our sun), orange and red (class M).

Hertzsprung-Russel diagram shows plot of stars which the distances from their parallaxes are

known. This diagram has axis of spectral class/colour/temperature and absolute brightness.

When the stars are plotted, a fairly narrow line (main sequence) is obtained. The brightness of

a star is measured at two different wavelengths where the different of the brightness is plotted

on the x-axis and one of the brightness is plotted on y-axis. The absolute brightness depends

on how much energy is produced in the star, this depends on the mass of the star (and what

nuclear reactions go on inside it), the mass determines its volume, the volume determines its

surface, and the surface, combined with the absolute brightness, determines the temperature.

Thus shows that surface temperature has a close correlation to absolute brightness. Stars

which do not lie on the main sequence are either giants (above) or dwarfs (below). A stellar

cluster is a group of stars that are close together, came into existence at the same time and

thus have the same age. By determining which stars still lie on the main sequence and which

stars already became giants, the age of the clusters can be determined.

Next, the standard candles method. These candles have known absolute brightness to be

compared with faint stars. First, Cepheids (variable stars), they periodically change their size,

temperature and brightness. To measure the distance of a cluster or a galaxy, find Cepheids in

it and measure their oscillation period. The oscillation period has an equivalent relation with

absolute brightness. The absolute brightness is compared to the apparent brightness to get the

distance. The second ‘candle’ is supernovae. Only supernovae type I can determine the

distance. It happens when two stars orbit each other (binary systems). If they are close

enough, one star will draw gases from the other (accretion) to its surface. If the accreting star

is a white dwarf, it will eventually collapse if its total mass exceeds a certain limit. Explosion

of carbon fusion will release a huge amount of energy which will disrupt the white dwarf. A

sudden brightness followed by a slow radioactive decay can be observed. Absolute brightness

of a supernova can be determined by observing the light received from the explosion and

determining the rate of the light to get dimmer. By comparing the absolute brightness and the

apparent brightness, the distance of the supernova can be obtained.

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Lastly, there is the cosmological red shift. It is the spectral lines which do not appear at the

usual places as it has slightly larger wavelength (which corresponds to redder). This can be

observed when the galaxies are moving away from us. The red shift (the speed they move

away) is directly proportional to the distance of the galaxies to us where [v = H x d, v =

speed, d = distance, H (Hubble parameter) = 70 kilometre/second/million parsec].

Reference:

Björn Feuerbacher, 2003. Determining Distances to Astronomical Objects.

http://www.talkorigins.org/faqs/astronomy/distance.html

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